Download Similar figures have the same shape, but their sizes may differ. If

3/6/13
Similar figures have the same shape, but their sizes may differ.
If polygons are similar then:
a) The ratios of the measures of corresponding sides are equal.
b) Corresponding angles are congruent.
c) The ratio of the perimeters equals the ratio of any pair of
corresponding sides.
D
A
B
C
E
F
AB BC AC
=
and
If !ABC ~ !DEF then =
DE EF DF
m!A = m!D, m!B = m!E, m!C = m!F
Congruence means same size and same shape.
SSS, SAS, ASA, AAS, and HL prove congruence.
Similar means same shape.
AAA proves similar triangles.
If there exists a correspondence between the vertices of two triangles such
that the three angles of one are congruent to the corresponding angles of
the other triangle, then the triangles are similar.
E
B
A
∆ABC ~ ∆DEF
C
AA proves similar triangles.
D
F
If there exists a correspondence between the vertices of two triangles such
that the two angles of one are congruent to the corresponding angles of the
other triangle, then the triangles are similar.
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SSS~
If there exists a correspondence between the vertices of two triangles such
that the ratios of the measures of corresponding sides are equal, then the
triangles are similar.
E
B
C
A
F
D
Given :
AB BC AC
=
=
, then !ABC ~ !DEF.
DE EF DF
SAS~
If there exists a correspondence between the vertices of two triangles such
that the ratios of the measures of two pairs of corresponding sides are
equal and the included angles are congruent, then the triangles are similar.
E
B
A
C
D
Given :
F
AB BC
=
and !B " !E, then #ABC ~ #DEF.
DE EF
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E
Given : N is the midpoint of ML,
F is the midpoint of TL.
Pr ove : !NFL ~ !MTL
N
T
Given : !BAT ~ !DOT,
OT = 15, BT = 12, TD = 9.
Find AO.
B
F
L
A
O
T
D
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Given: Parallelogram ABCD.
D
C
Prove: ∆BFE ~ ∆CFD.
F
A
B
E
4